Home / Optics & Photonics / Wave Optics / Diffraction Limit (Rayleigh Criterion)

Formula & Calculator

Diffraction Limit (Rayleigh Criterion)

Even a perfect lens cannot resolve two objects that are too close together, because light diffracts (spreads out) as it passes through the aperture. The Rayleigh criterion gives the minimum angle between two point sources that can just be distinguished. It depends on the wavelength of light and the diameter of the aperture. A larger aperture or shorter wavelength gives better resolution. This is why telescopes need big mirrors and why electron microscopes can see much smaller things than light microscopes.

Written by the Vorzep Team

Optics Wave Optics Resolution

Diffraction Limit CalculatorRayleigh Criterion · Optics

θmin = 1.22 · λ / D
θmin = angular resolution  ·  λ = wavelength  ·  D = aperture diameter
⟹ Solve⟷θmin, λ, D
rad
m
m
Please fix the errors above.
Solve for:
Presets:
θmin—
—
θmin: —λ: —D: —
✓ Copied!
Angular Resolution (θmin) Gauge—
High resolution (small θ) Moderate Low resolution (large θ)
θmin = 1.22 · λ / D  ·  All units must be consistent (SI: metres, radians)  ·  1 rad = 206265 arcseconds

Variables

Symbol Quantity Unit
θ_min Minimum resolvable angle radians
λ Wavelength of light m
D Aperture diameter m

What it means

The Rayleigh criterion gives the minimum angular separation that can be resolved by a circular aperture (like a telescope or microscope lens) due to diffraction. The factor 1.22 comes from the Airy disk. This is the fundamental limit on resolution. It is used to determine the resolving power of optical instruments. A larger aperture D gives better resolution. Understanding this is essential for astronomers, microscopists, and engineers designing high‑resolution imaging systems.

Worked example

Diffraction Limit (Rayleigh Criterion) – Two Detailed Examples

Real‑World
Scenario: A telescope has an aperture diameter D = 100 mm and observes light of wavelength λ = 550 nm. The minimum resolvable angle θ_min = 1.22 λ / D = 1.22 × 550×10⁻⁹ / 0.1 = 6.71×10⁻⁶ rad ≈ 1.38 arcseconds. This sets the theoretical resolving power; the telescope can distinguish two stars separated by at least this angle. The astronomer uses this to select aperture size for desired resolution.
ParameterValue
λ (nm)550
D (mm)100
1θ_min = 1.22 × 550e-9 / (100e-3) = 6.71e-6 rad
2Convert to arcseconds: 6.71e-6 × 206265 ≈ 1.384 arcsec
Result 1.38″ ✓ Resolving power
Scenario: A microscope objective with aperture D = 10 mm and wavelength λ = 500 nm has θ_min = 1.22×500e-9 / 0.01 = 6.1e-5 rad ≈ 12.6 arcseconds. This limits the smallest feature that can be resolved. The biologist uses this to understand the resolution limit of their microscope and to choose the appropriate objective for their sample.
ParameterValue
λ500
D10
1θ_min = 1.22×500e-9 / 10e-3 = 6.1e-5 rad
Result 12.58″ ✓ Microscope resolution
Insight: The Rayleigh criterion defines the minimum angular separation between two point sources that can be resolved. It depends on wavelength and aperture diameter. Larger aperture gives better resolution.

Common mistakes

  • Rayleigh criterion (diffraction limit): θ_min = 1.22·λ / D – the minimum angular resolution.
  • λ: Wavelength of light – in metres.
  • D: Aperture diameter – in metres.
  • θ_min: In radians – convert to arcseconds if needed (×206265).
  • Assumes: Circular aperture, uniform illumination, perfect optics.

Applications

The diffraction limit (Rayleigh criterion), θ_min = 1.22·λ/D, defines the minimum angular separation at which two point sources can be resolved by a circular aperture of diameter D. This is a fundamental limit for optical systems, including telescopes, microscopes, and cameras. Engineers use it to determine the resolving power of instruments, to set specifications for optical systems, and to assess the impact of aperture size on image quality. By increasing D, they can improve resolution. This formula is also used in astronomy to determine the resolving power of telescopes. Understanding the diffraction limit is essential for designing high‑resolution imaging systems.

  • Telescope and microscope resolution determination
  • Design of high‑resolution imaging systems
  • Understanding the limits of optical instruments
  • Evaluation of lens and mirror quality
  • Education on diffraction and resolution

Related calculators · Wave Optics

Recently updated formulas

Suggest an improvement

Found a mistake? Have a better example? Let us know.
You may send up to 3 suggestions per 24 hours.

Page details

1,885

Views
  • Published July 13, 2026
  • Last updated July 19, 2026